MinT - Best Known (27, 27+67, s)-Nets in Base 25

Best Known (27, 27+67, s)-Nets in Base 25

(27, 27+67, 200)-Net over F₂₅ — Constructive and digital

Digital (27, 94, 200)-net over F₂₅, using

t-expansion [i] based on digital (25, 94, 200)-net over F₂₅, using
- net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
    - a function field by GarcÃa and Quoos [i]

(27, 27+67, 4755)-Net in Base 25 — Upper bound on s

There is no (27, 94, 4756)-net in base 25, because

1 times m-reduction [i] would yield (27, 93, 4756)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 10220 818664 122003 860770 160600 338539 375416 960839 355873 945551 941274 818371 098166 352929 011958 634560 051225 725955 850318 071571 127460 102625 > 25⁹³ [i]